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self-organized-criticality
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Continuous Abelian Sandpile Model in two dimensional lattice
, Article International Journal of Modern Physics B ; Volume 25, Issue 32 , 2011 , Pages 4709-4720 ; 02179792 (ISSN) ; Lotfi, E ; Moghimi Araghi, S ; Sharif University of Technology
2011
Abstract
We investigate a new version of sandpile model which is very similar to Abelian Sandpile Model (ASM), but the height variables are continuous ones. With the toppling rule we define in our model, we show that the model can be mapped to ASM, so the general properties of the two models are identical. Yet the new model allows us to investigate some problems such as the effect of very small mass on the height probabilities, different boundary conditions
Chaos in sandpile models
, Article Modern Physics Letters B ; Volume 25, Issue 8 , 2011 , Pages 569-579 ; 02179849 (ISSN) ; Mollabashi, A ; Sharif University of Technology
Abstract
We have investigated the "weak chaos" exponent to see if it can be considered as a classification parameter of different sandpile models. Our simulation results show that the (Abelian) BTW sandpile model, the (non-Abelian) Zhang model, and the ("Abelian") Manna model possesses different "weak chaos" exponents, so they may belong to different universality classes. Finally, we show that getting off the critical point destroys this behavior in these models
The effect of the number of dissipative sites on a sandpile model
, Article Journal of Physics A: Mathematical and Theoretical ; Volume 48, Issue 8 , January , 2015 ; 17518113 (ISSN) ; Sebtosheikh, M ; Sharif University of Technology
Institute of Physics Publishing
2015
Abstract
In this paper we investigate the effect of the number of dissipative sites in an Abelian sandpile model. The dissipative sites are considered to be in the bulk rather than in the boundary. In such systems, statistics of avalanches smaller than a certain size obey a power law. We have seen that the exponents associated with these power law behaviors change slightly as the number of dissipative sites is decreased. We have found that the zero dissipation limits of these exponents are independent of size. Therefore we suggest that the previously-seen dependence of the exponent on the system size is because of the number of dissipative sites rather than the system size. Also it is observed that...
Abelian sandpile model: A conformal field theory point of view
, Article Nuclear Physics B ; Volume 718, Issue 3 , 2005 , Pages 362-370 ; 05503213 (ISSN) ; Rajabpour, M. A ; Rouhani, S ; Sharif University of Technology
2005
Abstract
In this paper we derive the scaling fields in c = -2 conformal field theory associated with weakly allowed clusters in Abelian sandpile model and show a direct relation between the two models. © 2005 Elsevier B.V. All rights reserved
Controlling cost in sandpile models through local adjustment of drive
, Article Physica A: Statistical Mechanics and its Applications ; Volume 534 , 2019 ; 03784371 (ISSN) ; Moghimi Araghi, S ; Sharif University of Technology
Elsevier B.V
2019
Abstract
In this paper we consider sandpile models and modify the drive mechanisms to control the size of avalanches. The modification to the drive mechanism is local. We have studied the scaling behavior of the BTW and Manna models. We have found that the BTW model is more sensitive to the modification than the Manna model. Furthermore we have assigned a cost function to each avalanche and have found an optimum value for the modification to arrive at the lowest cost © 2019
The Abelian Sand-pile Model (ASM) and Generalization to the Continuous State
, M.Sc. Thesis Sharif University of Technology ; Moghimi Araghi, Saman (Supervisor)
Abstract
The four-page article by Bak, Tang and Wiesenfeld in 1987 was a beginning to a new wave of physicists’ efforts to explain and describe the concept of complexity; a not-so-well-defined concept that resists against the reductionist tools and methods of physics. The Self-organized Criticality theory presented in that article via a simple model, known as sandpile model, was first of all an effort to explain the numerous occurrence of power law distribution in nature. SOC was introduced to tell us why so many natural phenomena like Earthquakes, landslides, forest fires, extinction and other seemingly non-related catastrophic events, more or less obey the scale-less power law distribution; A...
The Abelian sandpile model on the honeycomb lattice
, Article Journal of Statistical Mechanics: Theory and Experiment ; Volume 2010, Issue 2 , 2010 ; 17425468 (ISSN) ; Dashti Naserabadi, H ; Moghimi Araghi, S ; Ruelle, P ; Sharif University of Technology
2010
Abstract
We check the universality properties of the two-dimensional Abelian sandpile model by computing some of its properties on the honeycomb lattice. Exact expressions for unit-height correlation functions in the presence of boundaries and for different boundary conditions are derived. Also, we study the statistics of the boundaries of avalanche waves by using the theory of SLE and suggest that these curves are conformally invariant and described by SLE 2
Effect of Dissipation and Perturbation in Sandpile Model
, M.Sc. Thesis Sharif University of Technology ; Moghimi Araghi, Saman (Supervisor)
Abstract
Sandpile models are the simplest models to study self organized criticality (SOC). In these phenomena, system reaches its critical state and shows power law behavior without fine tuning of any external parameters. In nature, many examples of such phenomena has been observed such as earthquakes, rainfalls and heights of mountains. In SOC systems, always there is an input and an out put of energy. In sandpile models the dissipative sites that play the role of energy dissipation, are usualy put on the boundary. In this study we have considered sandpile models which have dissipative site in the bulk. We have controled the ratio of the dissipative sites to the number of whole sites and have shown...
Application of Conformal Field Theory in Abelian Sandpile Model
, Ph.D. Dissertation Sharif University of Technology ; Moghimi-Araghi, Saman (Supervisor) ; Rouhani, Shahin (Co-Advisor)
Abstract
The theory of self-organized criticality is originally introduced by Bak, Tang and Wiesenfeld as a general mechanism that can explain the behaviour of complex systems which naturally organize themselves into a critical state. They defined the sandpile model as an example of slowly driven and dissipative complex system to explain the concept of self-organized criticality. From the definition of the model, extensive work has been done on this model. Thanks to the Abelian property of the model, many statistical results have been derived exactly. Other properties of the model such as critical exponents and dynamical behaviors have been also studied using the mapping with some statistical models...
Sandpile Model on Height Parameters
, M.Sc. Thesis Sharif University of Technology ; Moghimi Araghi, Saman (Supervisor)
Abstract
Many statistical systems such as earthquakes, road trafcs, forest fres, neurocortical avalanches etc. exhibit self-organized criticality (SOC). In such systems without tuning extrenal parameters, the system arrives at criticality. During recent decades, a number of models are introduced which show the same charactristics. These models have made a platform to investigate the physics of self-organized criticality. Among them, sandpile models are the best known models. They exhibit critical behaviour such as scaling laws. Also in some of them conformal invariance is checked nummerically.Most of sandpile models deal with slope parameters, that is, the main dynamical parameters are the local...
Simulation of the Self-organized Critical Models on the
Human’s Brain Network
,
M.Sc. Thesis
Sharif University of Technology
;
Moghimi Araghi, Saman
(Supervisor)
Abstract
Self-organized critical phenomena are interesting phenomena which are ubiquitous in nature. Examples include mountain ranges , coastlines and also activities in the hu-man's brain. In these processes, without fine-tuning of any external parameter such as the temperature, the system exhibits critical behavior. In other words, the dynamics of the system, drives it towards an state in which long range correlations in space and scaling behaviors can be seen.The first successful model which could characterize such systems was BTW model, introduced by Bak , Tang and Wiesenfeld in 1987. This model, later named Abelian sandpile model, was very simple and because of this simplicity, a large amount of...
The Burridge-Knopoff Model on Rough Surfaces
,
M.Sc. Thesis
Sharif University of Technology
;
Moghimi Araghi, Saman
(Supervisor)
Abstract
Earthquakes are of self-organized critical phenomena, the phenomena that exhibit scaling behavior without tuning external parameters. A number of models have been proposed to describe such features of earthquakes, the most known one is the Burridge-Knopoff model. The Burridge-Knopof model is a spring-block system where the blocks slip on a plate which has friction and are attached through some other springs to a moving plate. Because of the moving plate the blocks become under increasing tension but do not move until the tension overcomes the static friction. As a result, the blocks will move and then stop repeatedly. These movements are avalanche-like and their intensity obeys a power-law...
The Effect of the Threshold Parameter on the Statistics of Neuronal Avalanches in the Rotational Model
, M.Sc. Thesis Sharif University of Technology ; Moghimi Araghi, Saman (Supervisor)
Abstract
There are experiments that conclude the brain is in the critical or near the critical region. These researches extract avalanches from the neuronal activity and then show that avalanche size (or duration) distribution obeys the power-law distribution. Defining avalanches from neuronal activity has some challenges. In some cases deciding the threshold (which determines the beginning and end of an avalanche) seems arbitrary or fine-tuned. In this thesis, we will show how different thresholds for defining avalanche and different time resolutions for defining neuronal activity can change avalanche size (or duration) distribution
Continuous Transition from Self-organized Criticality to Self-organized Bistability
, M.Sc. Thesis Sharif University of Technology ; Moghimi Araghi, Saman (Supervisor)
Abstract
”Self-organized criticality” is a conceptual term that has helped us describe cer- tain critical behaviors in nature over the past approximately thirty years. In systems exhibiting this characteristic, critical behavior emerges without the need for external parameter adjustments. The necessary mechanism to observe such phenomena is for the critical point to be a dynamical attractor. Based on this, other phenomena have been proposed in which the critical point is not an attractor; instead, a stable cycle forms around it. This mechanism has led to the emergence of a new concept known as ”self- organized bistability.” The primary model proposed for such a phenomenon is based on a sandpile...
Continuous transforming the BTW to the Manna model
, Article Physica A: Statistical Mechanics and its Applications ; Volume 419 , 2015 , Pages 196-202 ; 03784371 (ISSN) ; Moghimi Araghi, S ; Najafi, M. N ; Sharif University of Technology
Abstract
In this paper we define some stochastic perturbations of the BTW model which make it into Manna model. These models have a continuous parameter p, where p = 0 and 1 correspond to the BTW and Manna models respectively. We have investigated the properties of the statistical observables of the waves of avalanches for various values of p. Our data supports the expectation of a crossover in such systems; at large scales Manna model is dominant. Therefore we find strong evidence in favor of the universality classes being distinct. Also it is observed that the BTW fixed point is unstable when Manna-type perturbation is added to the model
Chaos in Sandpile Models With and Without Bulk Dissipation
, M.Sc. Thesis Sharif University of Technology ; Moghimi-Araghi, Saman (Supervisor)
Abstract
A complte set of characteristic parameters of the sandpile models is still unknown. We have studied the existence of ”weak chaos” critical exponent in different sandpile models and we have shown that it is a characteristic exponent of deterministic models. We have shown that BTW and Zhang models do not belong to the same universality class (contrary to Zhang’s previous conjecture and contrary to Ben-Hur & Biham’s results.) Also we have shown that directed models, specificly Ramaswamy-Dhar’s directed model form a different universality class. ”Weak chaos” exponent in also studied in massive models and we have shown that by increase of dissipation, the exponent decreases rapidly to an...
Transition from Abelian Sandpile Model to Manna Model
, M.Sc. Thesis Sharif University of Technology ; Moghimi-Araghi, Saman (Supervisor)
Abstract
In this research, we want to address the question of universality classes in BTW and Manna sandpile models. So far, number of works has been devoted to this issue but the the answer remained unsolved. We will try another approach to study this question by perturbing the original models. To this end, we introduce three models that have evolution rules between BTW model and Manna model. By simulating this models, we observe that in the presence of perturbation, the probability dis- tribution has two regimes of behaviour which are separated by a new characteristic scale. The regime of small avalanches is described by the exponent of BTW model and the regime of large avalanches by the exponent...
Effects of Drive on the Sandpile Models and Using it to Control Criticality
, M.Sc. Thesis Sharif University of Technology ; Moghimi Araghi, Saman (Supervisor)
Abstract
Self-Organized Criticality (SOC) is observed in different systems in nature. Hights of mountains earthquakes and traffic are a few examples. In such systems, without tuning external parameters critical behavior is found. In other words the dynamics of the system takes it towards criticality, where the correlation length is very large and scaling laws are observed. Due to scale invariance, events of any size are found; for example in the case of earthquakes, one can find earthquakes with any sizes in the earth. Each event causes a cost and larger events cause much larger cost. Therefore it would be of great importance if one could somehow destroy criticality and as a result diminish large and...
Fluctuations in the order of System Size in the Avalanche-Size Distribution of Sandpiles Model
, M.Sc. Thesis Sharif University of Technology ; Moghimi Araghi, Saman (Supervisor)
Abstract
Since the concept of Self-Organized Criticality was introduced in terms of BTW Sandpiles model, its major features have been known as broad power law distributions without any tuning parameters. In some selforganized critical systems like brain and neural networks, some evidences and experiments show a periodic or non-power law distribution of avalanches in addition to the power-law distributions of avalanches. In this thesis we try to observe the same phenomenon in the well-known SOC models, namely the BTW and Manna sandpile models. We have considered small lattice sizes with periodic boundary conditions and a small amount of dissipation. Within such conditions we observe a periodic-like...
Synaptic Plasticity in Brain Networks Based on Sandpile Models
, M.Sc. Thesis Sharif University of Technology ; Moghimi Araghi, Saman (Supervisor)
Abstract
Based on the large number of interacting cells and their abundant connections, human brain is a complex system able to produce interesting collective behaviors. Studying these collective behaviors needs special tools that potentially could be found in the context of the statistical physics of critical phenomena, as these tools are specifically developed for understanding the large-scale properties of physical systems. Starting with the introduction of the self-organized criticality in the late 80s, a number of physicists have tried to utilize this concept for explaining some aspects of the brain properties, such as memory and learnig. The observation of the neuronal avalanches in the early...